Rapha, nice but a bit pricey?

Maybe bellroy/maap collab?

Check the Mack workshop pouch dimensions. Not sure of Iphone plus size.

https://www.mackworkshop.com/products/jersey-pouch

Edit: he does custom stuff from time to time as well so email him if it isn't big enough.

This maybe? http://www.albioncycling.com/product/waterproof-pouch/

It's lovely, can't guarantee it fits monster phones though.

Muji

Does anyone know of a similar product to the essentials case that is big enough to fit an iPhone Plus?

Very un-Rapha, but try old fileofax cases/similar from charity shops. I wanted a similar case to make a tool kit for my motorbike and after weighing up a variety of pricey hipster options came across a fileofax which I gutted and fitted under my old motorbike seat perfectly.

edit: actually a quick google of the dimensions of the Personal and Compact Filofaxs shows they are:
171mm x 95mm
vs
158.1mm x 77.8mm for the iphone plus. They were/are made in nice Nappa and calf's leather of various colours.